CN116299465B - A Backprojection Imaging Method for Bistatic SAR Based on Subspace Time-Frequency Mapping - Google Patents

Abstract

The present invention relates to a bistatic SAR back-projection imaging method based on subspace time-frequency mapping, comprising: obtaining the two-dimensional time-domain echo signal of SAR; Perform acceleration compensation; use the first-order Keystone transform method in the range frequency domain, azimuth time domain to perform range walking correction on the echo signal after acceleration compensation to obtain the signal phase in the range Doppler domain; divide the imaging area into sub-regions to obtain several sub-regions; Perform range pulse pressure and residual range migration correction on the range Doppler domain signal phase in each subregion; construct a local Cartesian coordinate system in the imaging region; perform backprojection based on subspace time-frequency mapping in the local Cartesian coordinate system Imaging to obtain SAR images. This method improves the data processing efficiency of the algorithm, and reduces the complexity of the algorithm implementation process while maintaining the imaging accuracy.

Description

A bistatic SAR backprojection imaging method based on subspace time-frequency mapping

Technical Field

The invention belongs to the technical field of radar signal processing, and in particular relates to a bistatic SAR backprojection imaging method based on subspace time-frequency mapping.

Background Art

High-resolution SAR imaging is a key issue in radar signal processing, which aims to obtain high-resolution SAR radar images. The design of SAR imaging algorithms has an important impact on improving the resolution of SAR images. The bistatic forward-looking SAR configuration based on a highly maneuverable platform has the characteristics of strong mobility and separate transceiver platforms, which causes the echo signals of targets in the same range unit to no longer have the same range migration and Doppler characteristics, that is, they have complex two-dimensional space-variant coupling characteristics, which brings difficulties and challenges to the design of high-resolution imaging algorithms.

According to the imaging algorithm's processing method for echo signals, the bistatic SAR imaging algorithm mainly includes the time domain imaging algorithm and the frequency domain imaging algorithm. The time domain imaging algorithm mainly includes the time domain back projection algorithm, the time domain fast back projection algorithm and some extended algorithms. The frequency domain imaging algorithm mainly includes the range Doppler algorithm, the nonlinear variable scale imaging algorithm, the polar coordinate orientation algorithm, etc. Due to the complex two-dimensional space-varying characteristics, the traditional frequency domain algorithm brings the problem of large matching error to the design of the imaging matched filter, which ultimately leads to poor imaging accuracy of the imaging algorithm; compared with the frequency domain imaging algorithm, the time domain imaging algorithm has higher imaging accuracy, but its implementation complexity brings difficulties to the engineering application of the algorithm. In the monostatic SAR imaging algorithm, some scholars proposed a frequency domain back projection imaging algorithm, which performs interpolation in the rectangular coordinate system to avoid two-dimensional interpolation calculation and reduce the complexity of the imaging algorithm implementation. Due to the difference in echo signal characteristics between the bistatic SAR system and the monostatic SAR system, it is difficult to migrate and apply the monostatic imaging algorithm in the bistatic SAR system.

In summary, among the existing bistatic SAR imaging algorithms, the frequency domain imaging algorithm has the defect of poor imaging accuracy, and the time domain imaging algorithm has the defect of high complexity.

Summary of the invention

In order to solve the above problems existing in the prior art, the present invention provides a bistatic SAR backprojection imaging method based on subspace time-frequency mapping. The technical problem to be solved by the present invention is achieved through the following technical solutions:

The embodiment of the present invention provides a bistatic SAR backprojection imaging method based on subspace time-frequency mapping, comprising the steps of:

S1, obtaining the two-dimensional time domain echo signal of SAR;

S2, in the range frequency domain, azimuth time domain, using the time-varying acceleration information of the mobile platform to perform acceleration compensation on the two-dimensional time domain echo signal to obtain an acceleration-compensated echo signal;

S3, using the first-order Keystone transform method in the range frequency domain, azimuth time domain to perform range movement correction on the acceleration compensated echo signal to obtain the range Doppler domain signal phase;

S4, calculating the range migration correction residual between the first target point and the center point in the selected area according to the phase of the range Doppler domain signal, and dividing the imaging area into sub-areas based on the principle that the range migration correction residual between the first target point and the center point in the selected area is less than the range resolution, to obtain a plurality of sub-areas;

S5, performing range pulse pressure and residual range migration correction on the phase of the range Doppler domain signal in each sub-region to obtain an echo signal after range pulse pressure focusing;

S6. Constructing a local rectangular coordinate system in the imaging area according to the spatial geometric configuration of the transceiver platform of the bistatic SAR system;

S7. In the local rectangular coordinate system, the echo signal after the range-direction pulse pressure focusing in the sub-region is used to perform back-projection imaging based on subspace time-frequency mapping to obtain a SAR image.

In one embodiment of the present invention, the two-dimensional time domain echo signal is:

;

in, For distance to fast time, is the azimuth slow time, is the distance envelope function, is the azimuthal envelope function, is the slant range of the transmitted signal, is the linear modulation rate of the transmitted signal, is the speed of light, is the wavelength of the transmitted signal, Is an imaginary number.

In one embodiment of the present invention, step S2 comprises:

S21, performing range Fourier transform on the two-dimensional time domain echo signal to obtain echo signals in range frequency domain, azimuth and time domain;

S22. Construct an acceleration compensation filter using the time-varying acceleration information of the mobile platform:

;

in, is the sign of the acceleration compensation filter function, is the carrier frequency of the radar signal, is the distance frequency variable, is the modulus of the receiver’s acceleration, is the modulus of the transmitter’s acceleration, is the angle between the receiver velocity vector and the radar line of sight direction vector, is the angle between the transmitter velocity vector and the radar sight vector, is the azimuth slow time, is the higher-order remainder after series expansion, is the speed of light;

S23, using the acceleration compensation filter to compensate the echo signal in the range frequency domain, azimuth and time domain to obtain an acceleration compensated echo signal:

;

in, is the azimuthal envelope function, is the distance envelope function, is the linear modulation rate of the transmitted signal, For point Slow time in azimuth The slope distance history of time, , Slow time for azimuth The slant distance from the receiver to the target point at the moment, Slow time for azimuth The slant distance from the transmitter to the target point at the moment.

In one embodiment of the present invention, step S3 includes:

S31. Construct Keystone transformation factor:

;

in, Slow down time for the new orientation, is the azimuth slow time;

S32, using the Keystone transformation factor to perform range movement correction on the acceleration compensated echo signal to obtain a range Doppler domain signal phase:

;

in, is the carrier frequency of the radar signal, is the distance frequency variable, is the linear modulation rate of the transmitted signal, is the speed of light, The echo signal after acceleration compensation The Taylor series expansion coefficients of , is the sum of the slant distances from the receiver and transmitter to the imaging target point at the synthetic aperture center moment, , Slow down time for a new orientation Time point target The distance to the receiver radar, Slow down time for a new orientation Time point target Distance to the transmitter radar.

In one embodiment of the present invention, step S4 includes:

S41, calculating the residual range migration phase difference between the first target point and the center point in the selected area according to the range Doppler domain signal phase:

;

in, is the distance frequency variable, is the azimuth frequency variable, is the wavelength of the transmitted signal, is the carrier frequency of the radar signal, For selected area The Taylor series expansion coefficient of the second-order slope range history of the center point, For selected area The Taylor series expansion coefficient of the third-order slope range history of the center point, The echo signal after acceleration compensation The Taylor series expansion coefficients of , ;

S42, calculating the range migration correction residual between the first target point and the center point in the selected area according to the residual range migration phase difference;

S43, based on the principle that the distance migration correction residual between the first target point and the center point in the selected area is less than the distance resolution, all points in the selected area that meet the principle are divided into a sub-area, until the imaging area is divided into a plurality of sub-areas.

In one embodiment of the present invention, step S5 includes:

S51, designing a residual range migration correction filter, a range pulse compression filter and a secondary range pulse compression filter according to the mathematical representation of the range Doppler domain signal phase in the two-dimensional frequency domain phase; wherein,

The residual range migration correction filter is expressed as:

;

in, is the sign of the residual range migration correction filter function, is the distance frequency variable, is the azimuth frequency variable, , is the carrier frequency of the radar signal, is the wavelength of the transmitted signal, The echo signal after acceleration compensation The Taylor series expansion coefficients of ;

The distance pulse pressure filter is expressed as:

;

in, is the sign of the distance pulse pressure filter function, is the linear modulation rate of the transmitted signal;

The quadratic distance pulse pressure filter is expressed as:

;

in, is the symbol of the quadratic range pulse pressure filter function;

S52, using the residual range migration correction filter, the range pulse compression filter and the secondary range pulse compression filter, the phase of the range Doppler domain signal in each of the sub-areas is subjected to range-direction matched filtering to obtain an echo signal after range-direction pulse compression focusing.

In one embodiment of the present invention, step S6 includes:

According to the spatial geometric information of the transceiver platform of the bistatic SAR system, a second target point set having the same range characteristics in the imaging plane is determined;

According to the maximum inscribed rectangle of the second target point set, the local rectangular coordinate system of the sub-area is established by taking the tangent direction of the equidistant line at the center point of the sub-area as the first direction, the height direction as the second direction, and determining the third direction by a right-hand spiral based on the first direction and the second direction.

In one embodiment of the present invention, the conversion relationship between the local rectangular coordinate system and the bistatic SAR system imaging coordinate system is:

;

in, is a local rectangular coordinate system Any point in The center point of the sub-region coordinate, The imaging coordinate system of the bistatic SAR system is Any point in and Expressing the same point, is a local rectangular coordinate system of Axis and of The angle of the axis.

In one embodiment of the present invention, step S7 includes:

S71, performing a range-direction inverse Fourier transform on the echo signal after the range-direction pulse pressure focusing in the sub-region to obtain an echo signal in the range Doppler domain and an echo signal phase in the range Doppler domain, wherein:

The echo signal in the range Doppler domain is expressed as:

;

in, is the bandwidth of the transmitter when transmitting a linear frequency modulation signal, For distance to fast time, is the sum of the slant distances from the receiver and transmitter to the imaging target point at the synthetic aperture center moment, is the speed of light, is the azimuthal envelope function, is the azimuth frequency variable, is the echo signal phase in the range Doppler domain;

The echo signal phase in the range Doppler domain is expressed as:

;

in, is the wavelength of the transmitted signal, is the azimuth frequency variable, , The echo signal after acceleration compensation The Taylor series expansion coefficients of ;

S72, calculating the slant range history between the radar platform and the target according to the coordinate position of the third target point in the local rectangular coordinate system and the azimuth slow time:

;

in, is the azimuth slow time, is the coordinate position of the third target point in the local rectangular coordinate system, Slow time for azimuth Time receiver coordinate, Slow time for azimuth Time receiver coordinate, Slow time for azimuth Time receiver coordinate, Slow time for azimuth Time transmitter coordinate, Slow time for azimuth Time transmitter coordinate, Slow time for azimuth Time transmitter coordinate, is the height of the imaging target point;

S73, using the echo signal phase in the range Doppler domain and the slant range history between the radar platform and the target, perform frequency domain backprojection integration on the echo signal in the range Doppler domain of the sub-area to obtain an amplitude value of the third target point in the local rectangular coordinate system:

;

in, For sub-region The Doppler bandwidth, For point In the range Doppler domain, the echo signal is symbolized by ” indicates phase conjugation, For distance to fast time, For sub-region The azimuth frequency variable, The sub-region number.

Compared with the prior art, the present invention has the following beneficial effects:

The present invention divides the imaging area into different sub-areas in the range Doppler domain of the signal according to the range migration characteristics of the first target point and on the principle that the range migration correction residual of the selected area is less than the range resolution, thereby reducing the design error of the matched filter and the error of the range pulse pressure and the residual range migration correction, thereby reducing the influence of the two-dimensional space-variant characteristics of the bistatic SAR echo signal on the imaging quality and improving the imaging quality; by constructing a local rectangular coordinate system in the imaging area, since the data processing in the local imaging coordinate system has a larger effective area, the data processing efficiency of the algorithm is improved and the complexity of the implementation process of the back-projection algorithm is reduced; therefore, the method overcomes the difficulty brought by the complex two-dimensional space-variant coupling to the matched filter design of the imaging algorithm, avoids the defocusing problem brought by the two-dimensional coupling space-variant, improves the data processing efficiency of the algorithm, and reduces the complexity of the algorithm implementation process while maintaining the imaging accuracy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic flow chart of a bistatic SAR backprojection imaging method based on subspace time-frequency mapping provided by an embodiment of the present invention;

FIG2 is a geometric diagram of sub-region division provided by an embodiment of the present invention;

FIG3 is a diagram showing the spatial geometric configuration of a transceiver platform of a bistatic SAR system provided in an embodiment of the present invention;

FIG. 4 is a schematic diagram of constructing a local rectangular coordinate system provided by an embodiment of the present invention.

DETAILED DESCRIPTION

The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

Embodiment 1

Please refer to FIG. 1 , which is a schematic flow chart of a bistatic SAR backprojection imaging method based on subspace time-frequency mapping provided by an embodiment of the present invention.

The bistatic SAR backprojection imaging method based on subspace time-frequency mapping in this embodiment includes the following steps:

S1. Obtain the two-dimensional time domain echo signal of SAR.

Specifically, the echo signal is first recorded: the receiver and the transmitter are moved by being carried on a mobile platform, the transmitter illuminates the target area with radar and transmits a linear frequency modulation signal, and the receiver receives the echo of the target area and records the echo signal.

The recorded echo signal is two-dimensional data. The two dimensions of the data are fast time in range and slow time in azimuth. The two-dimensional time domain echo signal of SAR can be expressed as:

;

in, For distance to fast time, is the azimuth slow time, is the distance envelope function, is the azimuthal envelope function, is the slant range of the transmitted signal, is the linear modulation rate of the transmitted signal, is the speed of light, is the wavelength of the transmitted signal, Is an imaginary number.

S2, in the range frequency domain, azimuth time domain of the signal, using the time-varying acceleration information of the mobile platform to perform acceleration compensation on the two-dimensional time domain echo signal to obtain an acceleration-compensated echo signal. Specifically comprising the steps of:

S21. Perform range Fourier transform on the two-dimensional time domain echo signal to obtain echo signals in range, frequency domain, azimuth and time domain.

Specifically, from the expression of the SAR two-dimensional time domain echo signal, it can be seen that the key characteristic of the two-dimensional time domain echo signal lies in the slant range process of signal transmission . Slant range history of two-dimensional time domain echo signal It can be written as:

;

in, is the distance from the transmitter to the target without acceleration, is the distance from the receiver to the target without acceleration, is the modulus of the receiver’s acceleration, is the modulus of the transmitter’s acceleration, is the angle between the receiver velocity vector and the sight direction vector, is the angle between the transmitter velocity vector and the sight direction vector. Ignoring the change in acceleration in a synthetic aperture time, the above formula is converted to the azimuth slow time The slant range of the echo can be expressed as:

;

in, are the higher-order remainders after series expansion.

Perform range Fourier transform on the two-dimensional time domain echo data to obtain the echo signal in the range frequency domain azimuth time domain, which can be expressed as:

;

in, is the carrier frequency of the radar signal, is the distance frequency variable.

use Replace the above formula ,get:

;

The third phase of the above formula This is the impact of the acceleration of the transceiver platform on the signal spectrum.

S22. Using the time-varying acceleration information of the mobile platform, an acceleration compensation filter is constructed. The acceleration compensation filter function is expressed as:

;

in, is the sign of the acceleration compensation filter function;

S23, using the acceleration compensation filter to compensate the echo signal in the range frequency domain, azimuth and time domain to obtain an acceleration compensated echo signal.

Specifically, the acceleration compensation filter is used to uniformly compensate the influence of the acceleration of the transceiver platform on the signal spectrum in the range frequency domain, azimuth and time domain of the signal to obtain the acceleration compensated echo signal. , in azimuth slow time At the moment, the echo signal in the range frequency domain and azimuth time domain after acceleration compensation can be expressed as:

;

in, For point Slow time in azimuth The slope distance history at time is expressed as:

;

Slow time for azimuth The slant distance from the receiver to the target point at the moment, Slow time for azimuth The slant distance from the transmitter to the target point at the moment.

In order to obtain an accurate representation of the two-dimensional spectrum of the signal, the slant range history is expanded by Taylor series:

;

in, is the Taylor series expansion coefficient, is the sum of the slant distances from the receiver and transmitter to the imaging target point at the synthetic aperture center moment, It can be expressed as:

;

Slow time for azimuth Time point target The distance to the receiver radar, Slow time for azimuth Time point target Distance to the transmitter radar.

In this embodiment, the time-varying acceleration of the high-speed mobile platform causes the broadening or contraction of the echo signal spectrum, which is effectively corrected by the acceleration compensation method.

S3, using the first-order Keystone transform method in the range frequency domain, azimuth time domain to perform range movement correction on the acceleration compensated echo signal to obtain the range Doppler domain signal phase. Specifically including the steps:

S31. Construct Keystone transformation factor.

Specifically, the Keystone transform and its extended form can accurately correct the spatial variation of each order of range migration according to the spatial variation law. Therefore, the first-order Keystone transform is used to achieve complete correction of range migration, and the Keystone transform factor is constructed as:

;

in, Slow down time to the new direction.

S32, using the Keystone transformation factor to perform range movement correction on the acceleration compensated echo signal to obtain a range Doppler domain signal phase.

Specifically, after the acceleration-compensated echo signal is corrected for range movement by the Keystone transformation factor, the phase of the range Doppler domain signal can be expressed as:

;

in, The echo signal after acceleration compensation The Taylor series expansion coefficients of .

From the above range Doppler domain signal phase, it can be seen that the linear interpolation operation after Keystone transform directly changes the linear relationship between the range frequency and the new azimuth slow time, and the range movement of the hole edge in the echo is completely eliminated.

S4, calculating the range migration correction residual of the sub-region according to the phase of the range Doppler domain signal, and dividing the imaging region into sub-regions based on the principle that the range migration correction residual of the sub-region is less than the range resolution, to obtain a plurality of sub-regions. Specifically comprising the steps of:

S41, calculating the phase difference of the residual range migration between the first target point and the center point in the selected area according to the phase of the range Doppler domain signal.

Specifically, for the two-dimensional coupling characteristics of the two-dimensional time domain echo signal of the bistatic SAR, this embodiment provides the definition of the range migration correction residual of the sub-region based on the representation of the range Doppler domain signal after the first-order Keystone transform. After the acceleration-compensated echo signal completes the Keystone transform to correct the range migration, the phase of the range Doppler domain signal is transformed in azimuth using the stationary phase method, and the two-dimensional frequency domain phase of the echo signal is expressed as:

;

in, is the azimuth phase, is the residual range moving phase, is the distance pulse pressure phase, is the high-order phase that can be ignored in signal processing, is the azimuth frequency variable.

Determine a selected area in the imaging area , calculate the selected area The residual distance migration phase difference between the first target point and the center point in is:

;

in, For selected area The Taylor series expansion coefficient of the second-order slope range history of the center point, For selected area The Taylor series expansion coefficient of the third-order slope range history of the center point, It is expressed as:

.

S42: Calculate the range migration correction residual between the first target point and the center point in the selected area according to the residual range migration phase difference.

Specifically, the residual range migration phase difference is first subjected to an inverse Fourier transform in the azimuth direction to obtain the azimuth slow time and range frequency. Expressed, about The linear phase, the linear phase and the range migration residual are in a linear relationship, so the range migration correction residual between the first target point and the center point of the selected area can be calculated.

S43, based on the principle that the distance migration correction residual between the first target point and the center point in the selected area is less than the distance resolution, all points in the selected area that meet the principle are divided into a sub-area, until the imaging area is divided into a plurality of sub-areas.

Specifically, the division of sub-areas is based on the principle that the distance migration correction residual between the first target point and the center point in the selected area is less than the distance resolution, wherein the distance resolution is related to parameters such as the transmission signal bandwidth of the transmitter of the mobile platform and the motion parameters of the mobile platform. Combined with the phase difference representation of the residual distance migration described above, the sub-areas divided in the scene can be determined.

In one embodiment, for a selected area If the selected area The first target point in the selected area The center point range migration correction residual is smaller than the range resolution, and the selected area The first target point in the image is divided into a sub-region, and the selected region is searched All points that meet the above conditions are divided into the same sub-region; then, a new selected region is obtained in the remaining imaging area, and the distance migration correction residual between the target point and the center point in the new selected region is calculated, so as to perform sub-region division of other imaging areas.

After the sub-region division is completed, each sub-region not only completes the separation of the imaging area in the scene, but also completes the separation of the Doppler frequency domain. Please refer to Figure 2, which is a geometric diagram of the sub-region division provided by an embodiment of the present invention, wherein R represents a receiver and T represents a transmitter.

In view of the problem that the design error of the matched filter in the frequency domain imaging algorithm of the bistatic SAR system cannot be ignored, this embodiment establishes the concept of the range migration correction residual in the selected area. In the range Doppler domain of the signal, according to the range migration characteristic of the first target point, the imaging area is divided into different sub-areas on the principle that the range migration correction residual in the selected area is smaller than the range resolution, thereby reducing the design error of the matched filter, reducing the error of the range pulse pressure and the residual range migration correction, thereby reducing the influence of the two-dimensional space-varying characteristic of the bistatic SAR echo signal on the imaging quality, and improving the imaging quality.

S5, performing range pulse pressure and residual range migration correction on the phase of the range Doppler domain signal in each sub-region to obtain an echo signal after range pulse pressure focusing. Specifically comprising the steps of:

S51. Design a residual range migration correction filter, a range pulse compression filter and a secondary range pulse compression filter according to the mathematical representation of the range Doppler domain signal phase in the two-dimensional frequency domain phase.

Specifically, in the sub-region, the phase of the range Doppler domain signal obtained in step S3 is transformed in azimuth direction using the stationary phase method, and the two-dimensional frequency domain phase expression of the echo signal in the sub-region is obtained as follows:

;

in, The representative Order phase, Represents the stationary phase point.

Simplify it and Expand it, and we get:

;

in, .

Observing the above formula, the first item in the two-dimensional frequency domain phase of the echo signal in the sub-area is the range pulse pressure phase, the second item is the azimuth phase, the third item represents the range focus position and does not need to be processed, the fourth item is the residual range migration phase changed by the KT operation, and the fifth item is the secondary range pulse pressure phase.

Therefore, this embodiment completes the design of the residual range migration correction filter, the range pulse compression filter, and the secondary range pulse compression filter according to the mathematical expression of the two-dimensional frequency domain phase of the echo signal in the sub-region.

Among them, the residual range migration correction filter function can be expressed as:

;

in, is the sign of the residual range migration correction filter function.

The distance pulse pressure filter function can be expressed as:

;

in, is the sign of the range pulse compression filter function.

The quadratic distance pulse pressure filter function can be expressed as:

;

in, is the symbol of the quadratic range pulse compression filter function.

S52, using the residual range migration correction filter, the range pulse compression filter and the secondary range pulse compression filter, the phase of the range Doppler domain signal in each of the sub-areas is subjected to range matched filtering processing to obtain an echo signal after range pulse compression focusing, thereby completing the range focusing processing of all sub-area data.

S6. According to the spatial geometric configuration of the transceiver platform of the bistatic SAR system, a local rectangular coordinate system is constructed in the imaging area.

Firstly, according to the spatial geometric configuration of the transceiver platform of the bistatic SAR system, the second target point set with the same range characteristics in the imaging plane is determined; then, according to the maximum inscribed rectangle of the second target point set with the same range characteristics, the tangent direction of the equidistant line at the center point of the sub-area is taken as the first direction, the height direction is taken as the second direction, and the third direction is determined by the right-hand spiral according to the first direction and the second direction, and the local rectangular coordinate system of the imaging area is established.

Please refer to Figures 3 and 4. Figure 3 is a spatial geometric configuration diagram of the transceiver platform of the bistatic SAR system provided by an embodiment of the present invention, and Figure 4 is a schematic diagram of the construction of a local rectangular coordinate system provided by an embodiment of the present invention. The specific construction process of the above-mentioned local rectangular coordinate system is:

As shown in Figure 3, in the imaging coordinate system of the bistatic SAR system, the U direction is the altitude direction, the N direction is the north direction, and the E direction is the east direction; the curve AB represents the flight trajectory of the receiver, and the curve CD represents the receiving trajectory of the transmitter; is the transmitter speed, is the speed of the receiver; is the acceleration of the transmitter, is the acceleration of the receiver; point For imaging sub-area The coordinates of any point inside, For transmitter to sub-area Any point target The distance For receiver to sub-area Any point target The distance, point is the center point of the imaging sub-area. However, since the bistatic radar does not have azimuth translation invariance, the dark part in Figure 4 is essentially a set of second target points with the same range characteristics, and the maximum inscribed rectangle is represented by The maximum limit of this area that can be uniformly processed under the coordinate system. Obviously, a large part of the data in the area cannot be processed. The utilization efficiency can be expressed as:

;

in, is the area of the largest inscribed rectangle, It is the area occupied by the second target point set with the same distance characteristics.

Therefore, the sub-regions in Figure 3 were established The local rectangular coordinate system ,in The axis is the equidistant line where the sub-region center point is located at point The tangent direction of The axis is the height direction, The axis is determined by the right-hand screw rule. Coordinate system Axis and Coordinate system The axis has an angle The adjusted coordinate system can process data from a larger area, which helps improve data processing efficiency. The continuous increase of The processing efficiency of the coordinate system is ahead of The characteristics of the coordinate system become increasingly obvious.

Furthermore, assuming that the bistatic SAR system imaging coordinate system There is any point in , local rectangular coordinate system Any point in , and Indicates the same point, the center point of the sub-region The coordinates are , then the transformation relationship between the local rectangular coordinate system and the imaging coordinate system of the bistatic SAR system is the point The coordinates of The coordinate system can be expressed as:

.

This embodiment addresses the drawback of high implementation complexity in the time domain imaging algorithm of the bistatic SAR system. By establishing a local rectangular coordinate system based on the maximum inscribed rectangle in the imaging area, the data processing efficiency of the imaging algorithm is improved and the complexity of the back-projection algorithm implementation process is reduced because the data processing in the local imaging coordinate system has a larger effective area.

S7, in the local rectangular coordinate system, using the echo signal after the range pulse pressure focusing in the sub-region to perform back-projection imaging based on subspace time-frequency mapping to obtain a SAR image. Specifically comprising the steps of:

S71, performing range-direction inverse Fourier transform on the echo signal after range-direction pulse pressure focusing in the sub-region to obtain an echo signal in the range Doppler domain and an echo signal phase in the range Doppler domain.

Specifically, the echo signal in the range Doppler domain obtained by inverse Fourier transform of the range is expressed as:

;

in, is the bandwidth of the transmitter when transmitting a linear frequency modulation signal, is the sum of the slant distances from the receiver and transmitter to the imaging target point at the synthetic aperture center moment, is the speed of light, is the echo signal phase in the range Doppler domain, It is expressed as:

.

S72, based on the coordinate position of the third target point in the local rectangular coordinate system And the slant range history of the radar platform and the target is calculated in slow time in azimuth:

;

in, is the azimuth slow time, is the coordinate position of the third target point in the local rectangular coordinate system, Slow time for azimuth Time receiver coordinate, Slow time for azimuth Time receiver coordinate, Slow time for azimuth Time receiver coordinate, Slow time for azimuth Time transmitter coordinate, Slow time for azimuth Time transmitter coordinate, Slow time for azimuth Time transmitter coordinate, is the height of the imaging target point.

S73. Using the echo signal phase in the range Doppler domain and the slant range history between the radar platform and the target, perform frequency domain backprojection integration on the echo signal in the range Doppler domain of the sub-area to obtain an amplitude value of the third target point in the local rectangular coordinate system.

Specifically, according to the slant range history and the echo signal phase expression in the range Doppler domain, the echo signal in the range Doppler domain of the sub-region is integrated in the frequency domain by backprojection. The expression of the integration process can be expressed as:

;

in, For sub-region The Doppler bandwidth, For point In the range Doppler domain, the signal symbol " ” indicates phase conjugation, is the amplitude value of the third target point in the rectangular coordinate system, For distance to fast time, For sub-region The azimuth frequency variable, The sub-region number.

The amplitude value of the third target point in each sub-area in the local rectangular coordinate system can be obtained through the above integration process; after completing the imaging processing of all sub-areas, a high-resolution SAR image is finally obtained.

In summary, this embodiment analyzes the frequency domain focusing position and the corresponding azimuth spectrum characteristics of the target point in the sub-area, and proposes a bistatic SAR back-projection imaging algorithm based on subspace time-frequency mapping. Compared with other bistatic SAR system imaging algorithms, it overcomes the difficulties brought by complex two-dimensional space-variant coupling to the design of imaging algorithm matched filters, avoids the defocusing problem caused by two-dimensional coupling space-variant, performs frequency domain back-projection imaging in the constructed local rectangular coordinate system, improves the data processing efficiency of the algorithm, reduces the complexity of the algorithm implementation process, and improves the practicability in engineering.

Furthermore, the method of this embodiment can be applied to the forward imaging of the bistatic SAR system based on a mobile platform, and high-resolution forward imaging can be achieved under the conditions of complex spatial geometric configuration and high-mobility motion of the transceiver platform. Currently, the method of this embodiment is tested in the measured SAR echo data of the airborne flight, and it can avoid the defocusing problem caused by the serious two-dimensional coupling space variation in the echo signal, while maintaining the imaging resolution, reducing the complexity of the imaging algorithm implementation and improving the data processing efficiency of the algorithm.

The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims (7)

1. a kind of bistatic SAR back projection imaging method based on subspace time-frequency mapping, is characterized in that, comprises steps: S1. Obtaining a two-dimensional time-domain echo signal of the SAR; S2. In the distance frequency domain, azimuth time domain, using the time-varying acceleration information of the maneuvering platform to perform acceleration compensation on the two-dimensional time domain echo signal, to obtain an acceleration compensated echo signal; S3. Using the first-order Keystone transform method in the distance frequency domain, azimuth time domain to perform distance walking correction on the echo signal after the acceleration compensation, and obtain the signal phase in the range Doppler domain; step S3 includes: S31. Construct Keystone transformation factor: Among them, t _m is the new azimuth slowing time, t _a is the azimuth slowing time; S32. Using the Keystone transformation factor to perform range walking correction on the acceleration-compensated echo signal to obtain a range-Doppler domain signal phase: Among them, f _c is the carrier frequency of the radar signal, f _r is the frequency variable in the range direction, γ is the chirp frequency of the transmitted signal, c is the speed of light, k ₁ , k ₂ , and k ₃ are R in the echo signal after acceleration compensation Taylor series expansion coefficient of (t _a ; x, y, z), R ₀ is the sum of slope distances from the receiver and transmitter to the imaging target point at the center of the synthetic aperture, R ₀ =R _ro (0; x, y, z)+R _to (0; x, y, z), R _ro (0; x, y, z) is the new azimuth slow time t _m = 0 when the target (x, y, z) arrives at the receiver The distance of the radar, R _to (0; x, y, z) is the distance from the target (x, y, z) to the transmitter radar at the new azimuth slow time t _m = 0; S4. Calculate the range migration correction residual between the first target point and the central point in the selected area according to the signal phase in the range Doppler domain, and use the distance between the first target point and the central point in the selected area Based on the principle that the distance migration correction residual is smaller than the distance resolution, the imaging area is divided into sub-regions, and several sub-regions are obtained; S5. Perform range pulse pressure and residual range migration correction on the phase of the range Doppler domain signal in each of the sub-regions to obtain an echo signal after the range pulse pressure is focused; S6. Construct a local Cartesian coordinate system in the imaging area according to the spatial geometry configuration of the transceiver platform of the bistatic SAR system; S7. In the local Cartesian coordinate system, use the echo signals after the focused range pulse pressure in the sub-region to perform back-projection imaging based on subspace time-frequency mapping to obtain a SAR image; Step S7 includes: S71. Perform range inverse Fourier transform on the range-focused echo signal in the sub-region to obtain the echo signal in the range-Doppler domain and the phase of the echo signal in the range-Doppler domain, wherein , The echo signal in the range-Doppler domain is expressed as: Among them, B is the bandwidth when the transmitter transmits the chirp signal, t _r is the range fast time, R ₀ is the sum of the slant distances from the receiver and the transmitter to the imaging target point at the center of the synthetic aperture, c is the speed of light, w _a ( ) is the azimuth envelope function, f _a is the azimuth frequency variable, φ _a (f _a ) is the echo signal phase in the range Doppler domain; The echo signal phase in the range-Doppler domain is expressed as: Among them, λ is the wavelength of the transmitted signal, f _a is the azimuth frequency variable, k ₁ , k ₂ , k ₃ are the Taylor series expansion coefficients of R(t _a ; x, y, z) in the echo signal after acceleration compensation; S72. Calculate the slope distance history of the radar platform and the target according to the coordinate position of the third target point in the local Cartesian coordinate system and the azimuth slow time: Among them, t _a is the azimuth slow time, (x _p , y _p ) is the coordinate position of the third target point in the local Cartesian coordinate system, x _r (t _a ) is the x coordinate of the receiver at the time t _{a of} the azimuth slow time , y _r (t _a ) is the y coordinate of the receiver at the slow time t _a in the azimuth direction, z _r (t _a ) is the z coordinate of the receiver at the slow time t _a in the azimuth direction, and x _t (t _a ) is the azimuth direction The x-coordinate of the transmitter at slow time t _a , y _t (t _a ) is the y-coordinate of the transmitter at slow time t _a in azimuth, and z _t (t _a ) is the z-coordinate of the transmitter at slow time t _a in azimuth , z _p is the height of the imaging target point; S73. Using the phase of the echo signal in the range-Doppler domain and the slant-range histories of the radar platform and the target, perform frequency-domain backprojection integration on the echo signal in the range-Doppler domain of the sub-region, Get the magnitude value of the third target point in the local Cartesian coordinate system: Among them, B _a,i is the Doppler bandwidth of sub-region i, S(t _r ,f _a,i ; R(t _a ; x _p ,y _p )) is the point (x _p ,y _p ) at a distance of more than The echo signal in the Puller domain, the symbol "*" indicates phase conjugation, t _r is the range fast time, f _a,i is the azimuth frequency variable of sub-area i, and i is the sub-area number. 2. the bistatic SAR back projection imaging method based on subspace time-frequency mapping according to claim 1, is characterized in that, described two-dimensional time-domain echo signal is: Among them, t _r is the fast time in the range direction, t _a is the slow time in the azimuth direction, w _r () is the envelope function in the range direction, w _a () is the envelope function in the azimuth direction, R(t _a ) is the transmission time of the transmitted signal Slope distance history, γ is the chirp frequency of the transmitted signal, c is the speed of light, λ is the wavelength of the transmitted signal, and j is an imaginary number. 3. the bistatic SAR back projection imaging method based on subspace time-frequency mapping according to claim 1, is characterized in that, step S2 comprises: S21. Perform range-to-Fourier transform on the two-dimensional time-domain echo signal to obtain an echo signal in the range-frequency-domain, azimuth-time-domain; S22. Using the time-varying acceleration information of the maneuvering platform to construct an acceleration compensation filter: Among them, H ₁ is the symbol of the acceleration compensation filter function, f _c is the carrier frequency of the radar signal, f _r is the frequency variable in the range direction, a _r is the modulus value of the acceleration of the receiver, and _at is the modulus of the acceleration of the transmitter value, θ _r is the angle between the receiver velocity vector and the radar line of sight direction vector, θ _t is the angle between the transmitter velocity vector and the radar line of sight vector, t _a is the azimuth slow time, is the high-order remainder after series expansion, and c is the speed of light; S23. Using the acceleration compensation filter to compensate the echo signal in the distance frequency domain, azimuth time domain, and obtain an acceleration compensated echo signal: Among them, w _a () is the azimuth envelope function, w _r () is the range envelope function, γ is the chirp frequency of the transmitted signal, R(t _a ; x, y, z) is the point (x, y ,z) The slant range history at the azimuth slow time t _a , R(t _a ; x,y,z)=R _r (t _a )+R _t (t _a ), R _r (t _a ) is the azimuth R _t (t _a ) is the slope distance from the transmitter to the target point at slow time _{t a in} azimuth. 4. the bistatic SAR back projection imaging method based on subspace time-frequency mapping according to claim 1, is characterized in that, step S4 comprises: S41. Calculate the residual range migration phase difference between the first target point and the center point in the selected area according to the range Doppler domain signal phase: Among them, f _r is the frequency variable in the range direction, f _a is the frequency variable in the azimuth direction, λ is the wavelength of the transmitted signal, f _c is the carrier frequency of the radar signal, k _20,l is the second-order slant distance of the center point of the selected area l History Taylor series expansion coefficient, k _30,l is the third-order slant distance history Taylor series expansion coefficient of the center point of the selected area l, k ₁ ,k ₂ ,k ₃ are R(t _a ; Taylor series expansion coefficient of x, y, z), S42. Calculate a distance migration correction residual between the first target point and the central point in the selected area according to the residual distance migration phase difference; S43. Based on the principle that the distance migration correction residual between the first target point and the center point in the selected area is smaller than the distance resolution, divide all points in the selected area that satisfy the principle into a sub-group area until the imaging area is divided into several sub-areas. 5. the bistatic SAR back projection imaging method based on subspace time-frequency mapping according to claim 1, is characterized in that, step S5 comprises: S51. Designing a residual range migration correction filter, a range pulse pressure filter, and a secondary range pulse pressure filter according to the mathematical representation of the range Doppler domain signal phase in the two-dimensional frequency domain phase; wherein, The residual distance migration correction filter is expressed as: Among them, H ₂ is the sign of the residual range migration correction filter function, f _r is the frequency variable in the range direction, f _a is the frequency variable in the azimuth direction, f _c is the carrier frequency of the radar signal, λ is the wavelength of the transmitted signal, k ₁ , k ₂ , k ₃ are the Taylor series expansion coefficients of R(t _a ; x, y, z) in the echo signal after acceleration compensation ; The distance pulse pressure filter is expressed as: Among them, _H3 is the sign of the distance pulse pressure filter function, and γ is the chirp frequency of the transmitted signal; The secondary range pulse pressure filter is expressed as: Wherein, H ₄ is the symbol of the secondary range pulse pressure filter function; S52. Using the residual range migration correction filter, range pulse pressure filter, and secondary range pulse pressure filter, perform range-wise matched filtering on the phase of the range-Doppler domain signal in each of the sub-regions After processing, the echo signal after focusing on the pulse pressure in the range direction is obtained. 6. the bistatic SAR back projection imaging method based on subspace time-frequency mapping according to claim 1, is characterized in that, step S6 comprises: According to the spatial geometric information of the transceiver platform of the bistatic SAR system, a second set of target points with the same range characteristics in the imaging plane is determined; According to the largest inscribed rectangle of the second target point set, the tangent direction of the equidistance line where the center point of the sub-area is located at the center point of the sub-area is the first direction, and the height direction is the second direction, and according to the first direction The first direction and the second direction are determined by right-handed spiral to determine the third direction, and the local Cartesian coordinate system of the sub-region is established. 7. the bistatic SAR back projection imaging method based on subspace time-frequency mapping according to claim 6, is characterized in that, the transformation relation of described local Cartesian coordinate system and bistatic SAR system imaging coordinate system is: Among them, (x′, y′, z′) is any point existing in the local Cartesian coordinate system O _si -X _i Y _i Z, (x _oi , y _oi , z _oi ) is the coordinate of the center point O _si of the sub-region, (e,n,u) is any point existing in the imaging coordinate system O-ENU of the bistatic SAR system, (e,n,u) and (x′,y′,z′) represent the same point, and ψ is a local right angle The angle between the X _i axis of the coordinate system O _si -X _i Y _i Z and the E axis of O-ENU.